This is actually wrong. Some friends of mine proved that if you drop only S and Z pieces in an irrational ratio, the player is doomed irrespective of the dimensions of the board.
I can’t, but it was published in Eureka (Cambridge Maths Society/Archimedean journal) somewhere between 1988 and 1993 I think. I don’t know how to get old copies but they were all typeset in TeX.
The same people also proved (earlier) that with 3-ominos its a win for the player.
Incidentally, if you’re into cool maths that isn’t part of any major research line, Eureka is a great read.
The proof that Tetris is a win for the computer was published in Eureka 51 (1992) by Richard Tucker. (Someone else has posted a link to another paper proving this, but it's from 1997; Richard got there first.)
The proof that Tris is a win for the player was published in Eureka 51 (1991) by Adam Chalcraft. Richard and Adam definitely know one another and I would be unsurprised to learn that they talked to one another about this stuff, but the actual writeups in Eureka were by different people.
(Quite possibly a substantial amount of the thinking was done collectively at meetings of the "Puzzles and Games Ring", a sort of sub-organization of the Archimedeans (the student mathematical society at the University of Cambridge, which publishes Eureka).
